Conference: Advances in probability theory and interacting particle systems

This award supports the conference "Advances in probability theory and interacting particle systems" that will be held from the 26th-28th of August, 2024, at Harvard University. The conference has 21 confirmed speakers in very active and fundamental areas at the intersection of probability, analysis, and mathematical physics. The main aim is the rigorous study of universal phenomena for particle systems; to explain how random microscopic systems display predictable and statistically universal collective macroscopic behaviors. Large deviations are often key to understanding such problems, especially in large dimensions. Many problems remain in explaining how initial conditions and the details of the microscopic models govern the pre-stationary behavior. Many different approaches in this area will be represented at the conference, including spin-glasses, stochastic PDEs, and random walks in random environments. It is expected that this gathering will lead to cross-fertilization between these approaches, and inspire and inform a new generation of researchers. Many of the complex systems which will be discussed in this conference aim to describe real world phenomena and results proved for the mathematical models provide predictions applicable to the real systems. A key aspect of the conference proposal is centered on general methods for hydrodynamic limits and fluctuations of particle systems, in fixed or diverging dimensions. In the past, recent progress and the inclusion of new methods has shed light on many of the important questions related to the above. These include the understanding of p-spin models, a proof of the cutoff phenomena for the statistical physics models, fine asymptotics of mixing and cover times for general models, universality in random matrix theory. However, many of the original questions and conjectures remain open. Besides physical applications, complex systems (e.g., spin glasses, growth processes and random matrices) have found many applications in computer science, machine learning, data science, bioinformatics, chemistry, and even areas like ecology and earth science. The website for this conference is: https://www.math.harvard.edu/event/math-conference-honoring-srinivasa-varadhan/ This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.